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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

Posted on 11 April 2017 by David Kirtley

We occasionally receive excellent questions and/or comments by email or via our contact form and have then usually corresponded with the emailer directly. But, some of the questions and answers deserve a broader audience, so we decided to highlight some of them in a new series of blog posts.

The Keeling Curve (Figure 1) is one of the most iconic graphs illustrating modern climate change. Since 1958, the Keeling Curve has shown the increase in atmospheric CO2 from about 315 ppm to the present value of 405 ppm. CO2 measurements at Mauna Loa are taken hourly so this record has a very high time-resolution and is remarkably complete, even though there are occasional short gaps in the record.

Another iconic graph shows CO2 concentrations going back 800,000 years through eight of the Earth's ice age cycles (Figure 2). Our sudden anthropogenic CO2 spike is almost literally "off the charts" compared to the rest of the ice ages record. At no time during the last 800,000 years has there been any comparable increase in CO2 concentrations.

One of our readers (I'll call him A.B.) sent us an email asking about the time-resolution of the ice ages graph and how it compares to the resolution in the Keeling Curve:

Is there some study or dataset that shows the ice core samples with the same time resolution we see in modern measurements of CO2 such as the Keeling Curve; so that we can know for sure if there were any large-amplitude spikes of CO2 at earlier times (back to ~800 k yrs BP)?

The ice ages graph comes from measurements of CO2 in air bubbles trapped in ice cores drilled from the Antarctic ice sheets. These cores often have annual layers so it would be theoretically possible to get yearly samples of CO2, although the deeper (oldest) portions of the cores are vertically compressed, making the layers extremely thin. Still, even if all the annual layers were preserved, I doubt that scientists would sample all 800,000 layers (!) to produce such a high-resolution record. Surely, that would be overkill. I thought a CO2 sample taken every 10 or 20 or perhaps even 50 years would be high-res enough to get a good record of any fast changes in CO2 concentration, and would show any sudden spike like our current anthropogenic rise to 400 ppm.

A Look at the Literature

NOAA has a helpful webpage which points to Ice Core Data by Location.* Browsing through the list of Antarctic data I found a number of "high resolution" studies such as this one which only goes back about 22,000 years (Monnin et al. 2004). Figure 3 is a screenshot of this page which lists the data from the top of the EPICA Dome C core. The time-resolution jumps around a lot (the Age column), from as little as ~5-10 years between samples to ~100 years between samples. That is close to what I thought would be required to satisfy A.B.'s question, but not quite. The larger concern was that none of the longer ice core records seemed to have even this level of high resolution. The best I could find was a study by Luthi et al. (2008) (data, paper) which had a resolution of about 500 years for the oldest portion of the Dome C ice core.

Luckily, while writing the last "From the eMail Bag" post, I happened upon a scientist who has first-hand knowledge of Antarctica's ice cores, Dr Heidi Roop, who has "a particular interest in highly-resolved (annual to decadal) paleoclimate archives." I emailed her hoping she could point me to some truly high-res ice core data. Unfortunately, through no fault of her own, she could not. But she and some of her collegues did explain why such records are impossible to get from the oldest ice cores.

How to Make an Ice Core

The great polar ice sheets grow from layers of accumulated snowfall over thousands of years. The deeper layers of snow are slowly pressed into solid ice as more and more snow accumulates (see Figure 4, below). The porous upper layers of snow are called "firn" and range from ~40 - 120 meters deep. Inside the firn layer there is a network of pores (or air pockets) that are still connected to the atmosphere above it (the Convective and Diffusive Zones). At the bottom of the firn the snow is eventually compressed into ice and the air in the pore spaces is enclosed in bubbles and sealed off from further exchange with the atmosphere (the Lock-in Zone). The result is air bubbles which are much "younger" than the ice surrounding them. The age of the gas enclosed in bubbles minus the age of the ice gives us the Δ-age: gas age - ice age = Δ-age.

The firn can be open to the atmosphere for decades to centuries, depending on the local conditions at the ice coring site. At the West Antarctic Ice Sheet Divide (WAIS-Divide) site, which, at -31°C (-24°F), is relatively "warm" (by Antarctic standards at least) and has a lot of snow accumulation, the bubbles close off sooner than at colder sites with less snow accumulation, like Vostok and EPICA Dome C in East Antarctica.

Figure 4. Cross section of firn at a warm, high-snow-accumulation site (left) and a colder, low-accumulation site (right). The depths of firn layers and zones from actual ice core sites vary and are not the same thicknesses at each site as shown in this diagram. Illustration by jg.

Another complicating factor of the firn processes is that the gas in the bubbles does not really have a "single" age. Imagine a site where it takes 100 years from the time of snowfall until the snow reaches the Lock-in Zone trapping the air bubbles. The ice at the close-off depth is 100 years old but how old is the air in the bubbles? The firn was open to the atmosphere for ~100 years so the air in the bubbles could have come from any of those years. The result is an age distribution or range of most probable ages for the air in the bubbles.

Figure 5. Age distributions of CO2 molecules in the Law Dome DE08 firn from the surface to 75 meters, and in the ice at 80 meters. (Trudinger et al. 1997)

In the graph above the age distribution of the gas in the trapped bubbles (at 80 m deep) ranges from ~5 to ~25+ years wide, but the high point of the curve tells you the most probable age distribution, about 8-15 years wide. This graph is for a site which has very high snow accumulation, but for a site with very low snow accumulation the age distribution would be much broader, perhaps centuries wide.

Firn into Ice

Once the air is locked into bubbles the age distribution is essentially frozen as they are buried deeper and deeper into the ice sheet. But finding a particular age distribution for a particular bubble is not so straightforward. Scientists calculate age distributions using mathematical models with known firn parameters such as snow accumulation rates, temperature, density of the firn with depth, etc. Finding those known local parameters for modern firn is one thing, but knowing what those conditions were over thousands of years in the past is another.

Luckily, there is a short-cut for finding the age distribution. This is alluded to in a recent paper (Mitchell et al. 2015):

The bubbles are known to close off over a vertical ice age range [the Lock-in Zone] that corresponds to roughly 10% of the gas age-ice age difference, which intuitively should result in a gas age distribution width corresponding to 10% of the gas age-ice age difference [the Δ-age]. However, the observed smoothing of the trapped gas record often appears to be less than would be expected from this rate of gradual bubble closure.

So rather than 10%, a good rule-of-thumb, according to Dr. Christo Buizert, is to take 5% of the Δ-age to find the age distribution.

One more quirk affecting the age distribution is that two processes, diffusive transport of air through the firn pores and bubble close-off in the Lock-in Zone, have different effects on different cores. Spahni et al. (2003), found that these two processes have varying affects on the age distributions depending on site differences. For warm, high-accumulation sites the width of the age distribution is mainly governed by the diffusive mixing. And for colder, low-accumulation sites the width is mainly affected by the bubble close-off process.

The Ice Ages CO2 Graph

So what does all of this mean for the graph of CO2 during the ice ages (Figure 2)? The really deep, really old ice cores reaching back to 800,000 years ago come from sites with very large Δ-ages of thousands of years. The following graph shows various Δ-ages for various ice cores and how these Δ-ages can change slightly over time.

The oldest cores, from Vostok and EDC (EPICA Dome C), have the largest Δ-ages, ranging around 3000 to 6000 years, so the age-distributions would be around 150 to 300 years wide. This means that a sample of air from a bubble deep in one of these cores would not be from a specific year in the past but from a range of years spanning a few centuries. So it really would not matter if we took samples from each and every annual "layer" in the core (even if that were possible). We could never get that level of high-resolution because of the nature of the way the air is trapped in the ice. Each sample of CO2 from the ice cores is more like a short movie than a snapshot in time.

Samples taken 300 or so years apart should give a fairly fine-grained record of CO2, even with the smoothing caused by the age-distribution. But would that resolution be good enough to show a sudden spike in CO2 comparable to our modern anthro-spike? What about samples spaced further apart, say 500 or 1000 years apart? So just how finely sampled are the ice cores?

The vast majority of gaps between samples is less than 1000 years long (89%), and of these over half are 500 years long or less (65%). There is only one gap over 4000 years long, five gaps from 3000 to 4000 years long, 23 gaps from 2000 to 3000 years long, and 175 gaps from 1000 to 2000 years long. Would any of these millennia-long gaps be long enough to hide a spike in CO2 similar to our modern spike?

I put this question to Dr. Buizert who answered: "The possibility of a 50-year spike in CO2 up to 400 ppm (like the present one) during the last 800,000 years is vanishingly small, but admittedly not zero." The main reason for this is the nature of the carbon cycle, Dr. Buizert again:

CO2 has a long lifetime in the climate system of several thousands of years. Emitting CO2 like we're doing today can build up CO2 relatively fast in the atmosphere, but removing it again is a much slower process that involves chemical weathering of silicate rock and remineralization in the ocean...So given our understanding of the carbon cycle, a 50-year spike of 400 ppm CO2 is an impossibility. The CO2 cannot be removed fast enough, and inevitably the CO2 spike would persist for thousands of years, making it easily detectable with the ice core CO2 records that we do have.

Dr. David Archer's work (Archer et al. 2009) has shown that our current spike in CO2 will last for millennia. Even though the majority of the CO2 is absorbed by the oceans in the first ~500 years after a spike occurs, it takes 2 to 7 thousand years for the earth to absorb the rest of the spike. If such a spike had occurred during one of the longest gaps in the ice core record the measurements after the gap would be skewed higher.

Also, Dr. Buizert pointed out that even if such a spike did occur during one of these gaps there would have been "profound climatic consequences...and no evidence for this has been found in any climate archive (ice core or otherwise)."

Finally, Dr. Buizert notes:

Last, I think one could make the argument of large numbers. Between all ice core records, we have probably around 4000 data points of past CO2 concentrations - although admittedly, some of those records replicate one another. If such hypothetical 50-year spikes could indeed occur (despite the carbon-cycle arguments), we must have been incredibly unlucky not to hit at least one of them.

In Conclusion

Through the last eight ice age cycles atmospheric CO2 levels ranged from lows of ~175-200 ppm during the depths of each ice age, to highs of ~250-280 ppm during the warm interglacials. The magnitude of each of these variations was roughly a 90 ppm change in CO2 levels. These changes occurred over thousands, even tens of thousands, of years. The modern Keeling Curve shows a CO2 rise from ~315 ppm to ~405 ppm, or a 90 ppm increase (equal to the ice-ages variation), in only ~50 years. And if we consider the full length of our current spike, which began ~150 years ago from ~280 ppm, then we have a 125 ppm increase in CO2. In just a few more decades, if we continue to emit CO2 at current rates, we should reach the ~460 ppm mark which would bring us to a 180 ppm increase over pre-industrial levels—twice the natural range of variability seen in the ice age cycle. Such a sudden spike has never been recorded in ice cores from Greenland and Antarctica. Human emissions of CO2 are clearly unprecedented.

*Note about the NOAA webpage on Ice Cores. When I first started researching this topic the NOAA Ice Core Data by Location page linked directly to an individual study's data but sometime in February all of the links started going to this page: NOAA Paleo Data Search. This is not quite as helpful since you need to enter search terms but you eventually can find what you are looking for.

What's the reason Δ-age on Figure 6 varies so much with time? For example WDC core used to have Δ-age ~500 at 19ka and then dropped to 200 at 17ka. How did we find that Δ-age varies so much?

The article explains the Δ-age is the consequence of the surface parameters that dictate the speed of firm to ice transformation. Then it explains the Δ-age distribution. But it does not clearly explain how we know the actual value of Δ-age - or its mean value if we're talking about a statistical variable - as shown on Figure 6. Can the Δ-age be actually measured, e.g. by comparing the isotopic fingerprints of some components of gas boubles and surrounding ice?

Sorry to just throw papers at you but at the moment, and for the next 3-4 days, I won't have any time to dig any further. But I wanted to give you something in case you want to do some digging yourself.

Thanks for your pointers to the rellevant articles. Icidentally (or maybe not) Buizert 2015 is precisely about WDC (WAIS ice core), that I used as an example in my question, so I found it useful. Looks as they estimate Δ-age just on what you've said in the OP: firn densification modeling and ice-flow modeling. The age of ice is synchronized to thelayer-counted Greenland Ice Core Chronology (I did not know that counting of some ice core layers like this one in Greenland was possible like in dendrology). Another variable they used was a data set of δ15N-N2, which is a proxy for past firn column thickness.

The skeptic argument goes something like this: "the age of the air bubbles is spread out over hundreds of years, therefore if there were a large CO2 spike and the spike quickly disappeared, it would be invisible in the record. Therefore we don't know that our modern CO2 spike is anything unusual."

This article is a good start at responding to this claim. I suppose part of the response is that not a single climate scientist, including any of the contrarians (the 3%), has thought of any way that CO2 could disappear from the atmosphere as quickly as it has been added.

But it would be much better to have a direct answer like "we have high-resolution data for the last 12,000 years and no spikes have been observed, therefore no spikes exist in at least the last 12,000 years."

Unfortunately this article isn't clear enough to draw such a conclusion. One way it would be more clear is if it gave at least one example to demonstrate how to calculate the gas age distribution. This article implies that the majority of molecules in the Law Dome air bubbles have an age spread of 7 or 8 years because they are "about 8-15 years" old. But is this directly related to the Δ-age? The article says

The bubbles are known to close off over a vertical ice age range [the Lock-in Zone] that corresponds to roughly 10% of the gas age-ice age difference, which intuitively should result in a gas age distribution width corresponding to 10% of the gas age-ice age difference [the Δ-age]....

So rather than 10%, a good rule-of-thumb, according to Dr. Christo Buizert, is to take 5% of the Δ-age to find the age distribution.

Intuitively? It's not intuitive to me. So what does it mean? For starters, how is the concept of "age distribution" related to the 7 or 8 year spread we saw for Law Dome? The Δ-age was not provided for Law Dome. Can I infer from this that, if 50% of Law Dome air molecules have an 8-year spread, that the Δ-age for Law Dome is 8yrs / 5% = 160yrs? That doesn't sound right.

Great comments/questions, qwertie. You said: "not a single climate scientist, including any of the contrarians (the 3%), has thought of any way that CO2 could disappear from the atmosphere as quickly as it has been added."

Exactly. Which is what Dr. Buizert was saying. A sudden spike in CO2 would leave a mark in the record because everything we know about the carbon cycle tells us that the spike wouldn't "quickly disappear". Also, a sudden CO2 spike would have other effects on the ice core records: they would show a spike in temperatures which are also measured in the ice cores.

Your skeptic, in your example, wants to just look at the ice core CO2 measurements in isolation, without taking into account what is known about the carbon cycle.

You said: "Unfortunately this article isn't clear enough to draw such a conclusion. One way it would be more clear is if it gave at least one example to demonstrate how to calculate the gas age distribution."

Finding the "age distribution" isn't a very straight-forward process. This is all rather complicated stuff and I confess not to have a complete grip on all of it...especially all of the math involved. But conceptually I think I understand it (mostly). I'll try to explain it, but you may want to check the papers yourself. I would suggest these (you can find the links to them above in my list of refs.): Etheridge et al. 1996, Trudinger et al. 1997, Marcott et al. 2014. Also this one not listed: Buizert et al 2015.

When I was corresponding with Dr. Buizert I asked him where I could find age distributions for the various ice cores. He said that they are better known for firn air but not for the older air trapped deeper and deeper in the ice core bubbles. However the Delta-ages of ice cores are easier to find (see Figure 6 in OP), hence his "short-cut" for finding the age distributions: Δ-age x 5% = age dist.

Here is how these various things are related:

ice age - gas age = Δ-age

"Ice age" is easy to find, it can be found simpy by counting the layers in the ice core, like counting tree rings. And it is possible to tie this count into our calendar years by noting specific points in the core, like a layer of volcanic ash from an especially large and known volcanic eruption.

For the "gas age", we know that the air in bubbles is younger than the surrounding ice (described in the OP). But how much younger? Well that depends on the conditions (amount of snow accumulation and temperature) at the ice core location, and how long it takes for the bubbles to get "locked in" through the lock in zone. So to find the "gas age" scientists work backwards from the equation above, they start by calculating the Δ-age.

They find the Δ-age by using mathematical models using the specific firn conditions of the ice core location. With the modelled Δ-age and the known ice age, they can then use the equation to find the gas age. Here is an example of this technique, as described in the Marcott et al. 2014 paper from my ref. list:

"Gas ages were obtained by subtracting a modelled ice-age/gas-age difference (Δ-age) from the ice-age timescale. Δ-age was calculated using a dynamical firn-densification model with heat diffusion. The modelling is constrained by measurements of δ15N of N2, a proxy for past firn column thickness."

Let's say, for example, that our firn model gave us a Δ-age for the Law Dome ice core of 30 years. That means there would be a 30 year difference between the ice age and the gas age. Look at Figure 4 of the firn cross-section. The 30 year Δ-age is basically the time it takes for the top snow layer to get buried and eventually reach the close-off depth. At that depth any air in the ice is locked into bubbles and is closed off from further contact with the air in the firn above which is open to the atmosphere.

Back to Law Dome, a 30 year Δ-age is the actual value found in Etheridge et al. 1996. Here is a table from that paper:

Notice the last column: "Duration of Bubble Close-off Process". This is another way of describing the "age distribution" of the gas within the bubbles. Look again at Figure 4 of the firn cross-section. The bubble close-off process takes place in the "lock in zone". The length of time it takes for the air to become finally trapped in bubbles in the lock in zone defines the "age distribution". This is different for every ice core location, again, depending on snow accumulation, temperature, firn density, etc.

The time in the lock-in zone is roughly 10% of the time span given by the Δ-age. (But, again, this rough approximation would be different for each different ice core location.) So yes, the age distribution of the gas is directly related to the Δ-age. Hence, the quote from the Mitchell paper:

"The bubbles are known to close off over a vertical ice age range [the Lock-in Zone] that corresponds to roughly 10% of the gas age-ice age difference, which intuitively should result in a gas age distribution width corresponding to 10% of the gas age-ice age difference [the Δ-age]. However, the observed smoothing of the trapped gas record often appears to be less than would be expected from this rate of gradual bubble closure."

And my further comment: "So rather than 10%, a good rule-of-thumb, according to Dr. Christo Buizert, is to take 5% of the Δ-age to find the age distribution."

Back to Law Dome, again. Ten percent of the 30 year Δ-age would give an age distribution of only 3 years, not the 8-15 years I alluded to from Figure 5. Well, like I said, these are rough approximations.

The main point is to simply realize that the date of the CO2 in ice core bubbles cannot be pinpointed to a single year in the past. There is an age distribution or range of years that the gas is dated to. It may be very difficult to determine the exact width of a given ice core's age distribution, i.e. the span of years in the distribution, but we can get in the right ballpark.